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In this paper we introduce two new classes of inverses for square matrices, which are called 1Drazin (in short, 1D) inverse and Drazin1 (in short, D1) inverse. Next, we investigated the existence and uniqueness of 1D inverse and its dual D1 inverse. Some representation and characterizations of these inverses are derived. In addition to this, we obtain some properties of 1D and D1 inverses through idempotent and binary relations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a new faster iterative method, called the MNiteration process, for approximating a fixed point of continuous functions on an arbitrary interval. Then, a necessary and sufficient condition for the convergence of the MN-iteration of continuous functions on an arbitrary interval is established. We also compare the rate of convergence between the proposed iteration and some other iteration processes in the literature. Specifically, our main result shows that MN-iteration converges faster than NSP-iteration to the fixed point. We finally give numerical examples to compare the result with Mann, Ishikawa, Noor, SP and NSP iterations. Our findings improve corresponding results in the contemporary literature. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce new class of 2D-k-Laguerre-Konhauser polynomials, δL k,n(α,β) (x, y), which generalizes the 2D-Laguerre-Konhauser polynomials (see [18]). Then, we define a new family of bivariate k-Mittag-Leffler functions E k,α,β,δ(γ)(x, y) and establish the k-Riemann-Liouville double fractional integral and derivative of the functions E(γ) k,α,β,δ(x, y). Moreover, we introduce an integral operator kε(γ) α,β,δ;ω1,ω2;a+,c+ which contains the bivariate k-Mittag-Leffler functions E(γ) k,α,β,δ(x, y) in the kernel and investigate the semigroup property of this operator. Finally, the left inverse operator of the integral operator kε(γ) α,β,δ;ω1,ω2;a+,c+ is constructed. [ABSTRACT FROM AUTHOR]

This paper is a continuation of a recent work on a new norm, christened the (α, β)- norm, on the space of bounded linear operators on a Hilbert space. We obtain some upper bounds for the said norm of n × n operator matrices. As an application of the present study, we estimate bounds for the numerical radius and the usual operator norm of n × n operator matrices, which generalize the existing ones. [ABSTRACT FROM AUTHOR]

The paper introduces the notions of boundedness and convergence with speed for difference sequences, and characterizes certain matrix classes associating the sets of such classes of sequences involving the operator Δ and two speeds λ = (λk) and µ = (µk) ... The results obtained in this paper should easily extendible to difference sequences of higher orders, and even, in combination with multipliers. [ABSTRACT FROM AUTHOR]

Matrix factorizations have been widely used in recent years, especially in engineering problems, to facilitate performance-requiring computations. In this paper, we investigate some interesting relationships between some combinatorial matrices such as Pascal matrix, Stirling matrices and k-order Fibonacci matrices. We give factorizations and inverse factorizations of the Pascal and Stirling matrices via k-order Fibonacci matrices. Moreover, we derive various combinatorial properties by using relationships between these matrices. Finally, compared to previous studies, we present more general results for specific values of k. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new generalized inverses of matrices, namely, the hi;mi-core inverse and the (j, m)-core inverse. The (i, m)-core inverse of a complex matrix extends the notions of the core inverse defined by Baksalary and Trenkler [1] and the core-EP inverse defined by Manjunatha Prasad and Mohana [10]. The (j, m)-core inverse of a complex matrix extends the notions of the core inverse and the DMP-inverse defined by Malik and Thome [9]. Moreover, the formulae and properties of these two new concepts are investigated by using matrix decompositions and matrix powers. [ABSTRACT FROM AUTHOR]

In this paper,we study the existence and multiplicity of solutions for a perturbed three-point boundary value problem of Kirchhoff-type. The approach is based on variational methods and critical point theory.As applications of these methods,we get several multiplicity results for the problems under consideration. [ABSTRACT FROM AUTHOR]

Abstract. In this paper, we study Δ-convergence and strong convergence of the sequence generated by the extragradient method for pseudo-monotone equilibrium problems in Hadamard spaces. We first show Δ-convergence of the generated sequence to a solution of the equilibrium problem, then the strong convergence of Halpern regularization method is proved. Finally we give some examples where the main results can be applied. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain the spectrum, fine spectrum, approximate point spectrum, defect spectrum and compression spectrum of the operator ... on the sequence space c0 where the non-zero diagonals are the entries of an oscillatory sequence. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Fibonacci conditional sequence {fn} and the Lucas conditional sequence flng. We derive some properties of Fibonacci and Lucas conditional sequences by using the matrix method. Our results are elegant as the results for ordinary Fibonacci and Lucas sequences. [ABSTRACT FROM AUTHOR]

In this paper we introduce a class of quasipolar rings which is a generalization of J -quasipolar rings. Let R be a ring with identity. An element a ϵ 2 R is called 1-quasipolar if there exists p2 = p ϵ comm2(a) such that a + p is contained in δ(R), and the ring R is called δ-quasipolar if every element of R is δ-quasipolar. We use 1-quasipolar rings to extend some results of J-quasipolar rings. Then some of the main results of J-quasipolar rings are special cases of our results for this general setting. We give many characterizations and investigate general properties of 1-quasipolar rings. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove common fixed point theorems for two operators without the assumption of continuity on a set endowed with vector-valued b-metric and we also study the case of two vector-valued b-metrics. The well-posedness of the fixed point problem is also discussed and an application is presented for systems of operator equations in complete b-normed vector space. Our results improve and generalize theorems 2 and 5 of M. Boriceanu [5]. [ABSTRACT FROM AUTHOR]

In this paper, some algebraic properties of the joint k-numerical radius, joint k-radius and the joint k-norm of matrices are investigated. Moreover, using the joint higher numerical ranges of diagonal matrices which are convex polyhedrons, a description for the shape of the higher numerical ranges of matrix polynomials is given. [ABSTRACT FROM AUTHOR]

The paper introduces some sets of double lacunary invariant sequences defined by four dimensional RH-regular matrices and Orlicz functions. First we study some basic properties of such sets by equipping them with linear topological structure. Further, we investigate some relationships among such sets under different conditions and finally compare with a set of double lacunary statistically convergent sequences. [ABSTRACT FROM AUTHOR]

In this paper, the consimilarity of complex matrices is generalized for commutative quaternion matrices. In this regard, the coneigenvalue and coneigenvector for commutative quaternion matrices are defined. Also, the existence of solution to the some commutative quaternion matrix equations is characterized and solutions of these matrix equations are derived by means of real representations of commutative quaternion matrices. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of linear systems of neutral differential equations with delay. Assuming the linear parts to be given by pairwise permutable matrices, representation of a solution of a nonhomogeneous initial value problem using matrix polynomial of a degree depending on time is derived. Examples illustrating the obtained results are given. [ABSTRACT FROM AUTHOR]

A selection of ring theory papers by Jenő Szigeti is reviewed with an emphasis on aspects related to matrix algebras. [ABSTRACT FROM AUTHOR]

Let L denote operator generated in L2(R+,E) by the differential expression l(y) = -y"+Q(x)y, x ∊ R+ :=[0,∞); and the boundary condition (A0+A1)Y' (0,λ)-(B0+B1λ)Y(0,λ)=0, whereQ is a matrixvalued function and A0; A1; B0; B1 are non-singular matrices, with A0B1 - A1B0 ≠ 0: In this paper, we investigate the principal functions corresponding to the eigenvalues and the spectral singularities of L. [ABSTRACT FROM AUTHOR]

Let Mn be the algebra of all n × n matrices with entries in the field of real numbers. For a matrix Z ∊ Mn, it is said that a linear map T : Mn →Mn is multiplicative at Z if T (AB) = T (A)T (B) whenever AB = Z. In this paper we investigate some properties of multiplicative mapping at invertible matrices and also we characterize all multiplicative isomorphisms at invertible matrices. Then we give an example to show that multiplicativity at I doesn't imply multiplicativity on Mn, where I ∊ Mn is the identity matrix. [ABSTRACT FROM AUTHOR]

In this paper, we extend two curious divisibility properties for the general second order linear recurrence {Un(p,q)}. We also give new recursive identities for the general second linear recurrences {Un(p,q)} and {Vn(p,q)}. These results generalize the results given by E. Kılıç, "A matrix approach for generalizing two curious divisibility properties", Miskolc Math. Notes, vol. 13., No. 2, pp. 389-396, 2012. [ABSTRACT FROM AUTHOR]

Let n×n complex matrices P and Q be nontrivial generalized reflection matrices, i.e., P* = P = P-1 ≠ In, Q* = Q = Q-1 ≠ In. A complex matrix A with order n is said to be a (P, Q) generalized anti-reflexive matrix, if PAQ = -A. We in this paper mainly investigate the (P, Q) generalized anti-reflexive maximal and minimal rank solutions to the system of matrix equation AX = B. We present necessary and sufficient conditions for the existence of the maximal and minimal rank solutions, with (P, Q) generalized anti-reflexive, of the system. Expressions of such solutions to this system are also given when the solvability conditions are satisfied. In addition, in correspondence with the minimal rank solution set to the system, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm has been provided. [ABSTRACT FROM AUTHOR]

In this paper, we give a recurrence relation for the Tribonacci numbers with indices in aritmetics progression, {Trn+s} for 0 ⩽ s < n. We find sums of {Trn} for arbitrary integer r via matrix methods. [ABSTRACT FROM AUTHOR]

Let X0,X1,…,Xq be left invariant real vector fields on the homogeneous group G, satisfying Hörmander's condition on ℝN . Assume that X1,…,Xq are homogeneous of degree one and X0 is homogeneous of degree two. In this paper we consider the following hypoelliptic operator with drift ... where (aij) is a q × q positive constant matrix and a0 ≠ 0, and obtain Global Hölder estimates for L on G by establishing several estimates of singular integrals. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the necessary and sufficient conditions for having the maximum principle and existence of positive solutions for some cooperative systems involving Schrödinger operators defined on unbounded domains. Then, we deduce the existence of solutions for semi-linear systems. Finally we discuss the generalized maximum principle (ϕq- positivity) for non-cooperative systems. [ABSTRACT FROM AUTHOR]

J. C. Robson has investigated the ideal In of all polynomials in the free associative algebra R(χ) over a non-commutative ring R generated by χ and the n² entries of an n × n matrix α = (αij), which are satisfied by . He found four cubics generating the ideal for n D 2 and proved its finite generation for any n. Ts. Rashkova has considered the ideal I2 for matrix algebras with involution over a noncommutative ring and over a field of characteristic zero. In the paper the ideal I3 is described for some special upper triangular matrices over a field of characteristic 0. The T -ideal T (U2(G)) is investigated as well for G denoting the infinite dimensional Grassmann algebra. [ABSTRACT FROM AUTHOR]